Combining Smart Factors Momentum and Market Portfolio
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The Active vs Passive: Smart Factors, Market Portfolio or Both?
Matus Padysak
- SKComenius University Bratislava
- ?Comenius University - Faculty of Mathematics, Physics and Informatics
- ?Quantpedia.com
Strategy in a nutshell
The investment universe consists of factors from the Alpha Architect’s Factor Investing Data Library (factor for all major investment styles such as Value, Quality, Momentum, Size and Volatility) based on the top 1500 US stocks. Firstly construct the fast and slow signals for each factor. The fast signal is the past one-month return, and the slow signal is the past twelve-months return. For each type of signal, to obtain the weights, cross-sectionally rank signals’ based on their absolute values. The weight for the individual slow or fast signal is equal to the corresponding rank divided by the sum of all ranks and multiplied by the signal’s sign (equations 3 and 4 in the paper). For the dynamically blended strategy (smart factors strategy), each factor has a final weight of three-quarters of the weight of fast signal plus one-quarter of the weight of slow signal (equation 12). Nextly, consider the top 1500 US stocks as the market portfolio. The combined smart factors and market strategy finds the weights of the market and factor portfolio using past moving averages of the returns. The combined strategy looks back on the past twelve months, and twelve MAs of the returns. Suppose the MA for active investing (factor momentum) is larger than MA for market portfolio, then the active investing scores one point. Otherwise, the market portfolio gets one point. Therefore, each month, the weight of the factor momentum and market portfolio is determined by the number of “winning” (loosing) moving averages (equations 13 and 14). The strategy is rebalanced monthly.
Economic rationale
Firstly, the functionality of factor strategies was proven by numerous academic researches. The same could be said about the momentum in factors since both the time-series and cross-sectional momentum strategies are well-examined and proved to be functional. The factor momentum also solves the problem of underperforming factors because of the wrong portfolio sort (for example, when growth outperforms value or big size outperforms small size).
The blending of the factor seems to be important because the slow signals tend to be unreactive to changes in trend, and fast signals are often false alarms. Therefore, the weight of the factors should be adjusted based on signal interreactions. Lastly, the dynamical weights based on the strength of the signals is also a widely utilized approach that was found to be effective also in the factor universe.
Although the active factor strategy largely outperforms naive equal-weighting of the factors or signals alone, it would have been largely beaten by the market. However, the active factor strategy and market are negatively correlated. This correlation is statistically significant using a robust non-parametric test, and this result suggests that the two portfolios could be combined to achieve the best of the two approaches. The backtest confirms this theory, since the combined strategy using moving averages, has the largest return, the lowest volatility or drawdown, and the returns distribution is much more favourable.
Backtest performance
Full Python code
from AlgoLib import *
import numpy as np
#endregion
class CombiningSmartFactorsMomentumandMarketPortfolio(XXX):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.symbols = {
'momentum' : 'US_EQUAL_DECILE_1500_12_2m_L_S',
'value' : 'US_EQUAL_DECILE_1500_B_M_L_S',
'quality' : 'US_EQUAL_DECILE_1500_ROA_L_S',
'size' : 'US_EQUAL_DECILE_1500_Size_L_S',
'volatility' : 'US_EQUAL_DECILE_1500_Volatility_L_S',
}
# monthly price data
self.data = {}
self.long_period = 13
self.short_period = 2
self.max_missing_days:int = 5
self.monthly_returns = {}
self.monthly_returns_period = 12
for symbol, equity_symbol in self.symbols.items():
data = self.AddData(USEquity, equity_symbol, Resolution.Daily)
data.SetLeverage(10)
data.SetFeeModel(CustomFeeModel())
self.data[symbol] = RollingWindow[float](self.long_period)
self.market = self.AddEquity("IWM", Resolution.Daily).Symbol
self.data[self.market] = RollingWindow[float](self.short_period)
self.monthly_returns['smart_factors'] = RollingWindow[float](self.monthly_returns_period)
self.monthly_returns['market'] = RollingWindow[float](self.monthly_returns_period)
self.recent_month:int = -1
def OnSecuritiesChanged(self, changes):
for security in changes.AddedSecurities:
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(5)
def OnData(self, data):
# store factor monthly prices
for symbol, equity_symbol in self.symbols.items():
if equity_symbol in data and data[equity_symbol]:
price = data[equity_symbol].Value
self.data[symbol].Add(price)
# store market prices
if self.market in data and data[self.market]:
market_price = data[self.market].Value
self.data[self.market].Add(market_price)
if self.recent_month == self.Time.month:
return
self.recent_month = self.Time.month
slow_momentum = {}
fast_momentum = {}
# calculate both momentum values
for symbol, equity_symbol in self.symbols.items():
if self.Securities[equity_symbol].GetLastData() and (self.Time.date() - self.Securities[equity_symbol].GetLastData().Time.date()).days <= self.max_missing_days:
if self.data[symbol].IsReady:
slow_momentum[symbol] = self.data[symbol][0] / self.data[symbol][self.long_period-1] - 1
fast_momentum[symbol] = self.data[symbol][0] / self.data[symbol][1] - 1
total_weight = {}
if len(fast_momentum) != 0:
# momentum ranking
# weights
rank_sum = sum([x for x in range(1, len(slow_momentum)+1)])
sorted_by_slow_momentum = sorted(slow_momentum.items(), key = lambda x: abs(x[1]), reverse = False)
slow_weight = {}
for i, (symbol, momentum) in enumerate(sorted_by_slow_momentum):
rank = i+1
slow_weight[symbol] = (rank / rank_sum) * np.sign(momentum)
sorted_by_fast_momentum = sorted(fast_momentum.items(), key = lambda x: abs(x[1]), reverse = False)
fast_weight = {}
for i, (symbol, momentum) in enumerate(sorted_by_fast_momentum):
rank = i+1
fast_weight[symbol] = (rank / rank_sum) * np.sign(momentum)
# total weight
for symbol, equity_symbol in self.symbols.items():
if symbol in slow_momentum and symbol in fast_momentum:
s_weight = slow_weight[symbol]
f_weight = fast_weight[symbol]
total_weight[symbol] = 0.75*f_weight + 0.25*s_weight
# retrun calculation for market and smart factors
if self.data[self.market].IsReady:
market_return = self.data[self.market][0] / self.data[self.market][1] - 1
self.monthly_returns['market'].Add(market_return)
# smart factor return calculation
smart_factors_return = 0
for symbol, momentum_1M in fast_momentum.items():
if symbol in total_weight:
w = total_weight[symbol]
symbol_ret = w*momentum_1M
smart_factors_return += symbol_ret
if smart_factors_return != 0:
self.monthly_returns['smart_factors'].Add(smart_factors_return)
score = {}
traded_weight = {}
# calculate 12 SMA's
if self.monthly_returns['smart_factors'].IsReady and self.monthly_returns['market'].IsReady:
score['smart_factors'] = 0
score['market'] = 0
for sma_period in range(1, 13):
factor_returns = [x for x in self.monthly_returns['smart_factors']][:sma_period]
market_returns = [x for x in self.monthly_returns['market']][:sma_period]
factor_mean_return = np.mean(factor_returns)
market_mean_return = np.mean(market_returns)
if factor_mean_return > market_mean_return:
score['smart_factors'] += 1
else:
score['market'] += 1
total_score = score['market'] + score['smart_factors']
if total_score != 0:
traded_weight['market'] = score['market'] / total_score
traded_weight['smart_factors'] = score['smart_factors'] / total_score
# order execution
# market
self.SetHoldings(self.market, traded_weight['market'])
# smart factors
for symbol, equity_symbol in self.symbols.items():
if symbol in total_weight:
w = total_weight[symbol]
self.SetHoldings(equity_symbol, traded_weight['smart_factors'] * w)
class USEquity(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/equity/us_ew_decile/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
# File example.
# date;equity
# 1992-01-31;0.98
def Reader(self, config, line, date, isLiveMode):
data = USEquity()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(';')
# Prevent lookahead bias.
data.Time = datetime.strptime(split[0], "%Y-%m-%d") + timedelta(days=1)
data.Value = float(split[1])
return data
# Custom fee model
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))